What is the impact of using multiple BMUs for self-organizing maps?
The following is my intuition about the behavior of the algorithm considering your question, based on my knowledge and experience with single BMU SOMs. I didn't verify it experimentally.
At early stages of training:
It should disturb the SOM topology preserving properties, as you're assigning the same pattern to different (and probably distant) locations in the lattice, making the distribution multimodal. This is not terrible on its own, as different positions could encode different relationships to neighbors, overcoming the limitations of a single 2D/3D neighborhood. But if your SOM is not large enough, the multiple modes may collapse, resulting in unimodal distributions covering large portions of the map, wasting space. It all depends on your training schedule.
At later stages of training:
If you started with a single BMU at early stages, it wouldn't provide any meaningful impact, as a SOM, by definition, clusters similar patterns at close positions of its lattice. In other words, the neurons closest to your input are already inside the BMU update radius. If you trained with multiple BMUs since the beginning, you would keep finding / activating the multiple maxima of your multimodal distributions for each pattern. The dimensionality reduction would become even more nonlinear than it already is with single BMUs. This may or may not be a problem, depending on your application.